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Worksheet on Remainder Theorem

Practice the questions given in the worksheet on Remainder Theorem.


1. Use the Remainder Theorem, find the remainder when 4x3 - 3x2 + 2x - 4 is divided by x + 1.

2. If p(y) = y3 + y2 - 2y + 1, using Remainder Theorem, find the remainder, when p(y) is divided by (y – 3), find the value of p(a).

3. Find the remainder (without division) when

(a) x2 - 2x + 4 is divided by x - 1

(b) 2x3 - 3x2 + 7x - 8 is divided by x - 1


4. Use the Remainder Theorem, find the remainder when x4 - 3x2 + 4x - 12 is divided by x - 3.


5. Find the remainder (without division) when

(a) x3 + 4x + 2 is divisible by x + 2

(b) 4x3 - 3x2 + 5x + 4 is divided by 2x + 1

(c) 4x3 + 5x2 + 6x - 7 is divided by 2x - 1


6. What number should be added to x2 + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?

7. Use the Remainder Theorem, find the remainder when 4x3 - 3x2 + 2x - 4 is divided by x + 1.

8. What number should be subtracted from 3x2 + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?

9. Use the Remainder Theorem, find the remainder when x6 + 3x2 + 10 is divided by x - 2.

10.  Find a if the remainder is a when x3 + 3x2 - ax + 3 is divided by x - 2.

11. If the polynomials ax3 + 4x2 + 3x – 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.

12. Find the value of k if the remainder is -3 when kx3 + 8x2 - 4x + 10 is divided by x +1.

13. If both ax3 + 2x2 - 3 and x2 - ax + 4 leave the same remainder when divided by x - 2, find a.


Answers for the worksheet on Remainder Theorem are given below:


Answers:


1. -13

2. 31, a3 + a2 - 2a + 1

3. (a) 3

(b) -2


4. 54

5. (a) -14

(b) 14

(c) -94


6. -11

7. -13

8. 214

9. 86

10. 233

11. a = -1.

12. 25

13. 310

● Factorization















10th Grade Math

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